Author: Suman Ganguli (Page 1 of 11)

Schedule

• WebWork: “Derivatives – Logarithmic” and “Derivatives – Implicit” extended to Fri Dec 13
• Exam #2 corrections (optional) are due tomorrow (Wed Dec 11)
• Final Exam Review– hand in written solutions to the following exercises (on Wed Dec 11 if you have them finished, but if you need more time I will take them next week as well):
  • #5 (logarithmic differentiation)
  • #7 (implicit differentiation)
  • #8 (tangent lines, linear approximations and differentials)
  • #16 & #17 (optimization)
  • #18 (using critical pts, intervals of increasing/decreasing, and intervals of concavity for sketching a graph)
    • note that we set up #8 and #17 in class (see below), and we set up #5 and #7 last week
    • for #18, follow the example we did in class last Wednesday, and recapped in this class (see below)
    • the Final Exam Review exercises (including limited solutions) is available as a pdf on OpenLab Files
• Exam #3:
  • this will cover the topics from the Final Exam Review listed above (plus related rates, which we will cover tomorrow)
  • take-home exercises for 50% of this exam will be handed out in class on Wed Dec 11, to be handed in on Monday Dec 16
  • there will also be a short in-class exam on Monday Dec 16, for the remaining 50%; these exercises will be similar to the take-home exercises
  • we will use half the class period on Mon Dec 16 to do some additional review for the final
• Final exam: Wednesday Dec 18

Boardshots

We recapped the examples previous class on graph-sketching using the first and second derivatives, looking at a cubic polynomial f(x). We discussed these figures from Sec 4.5 which illustrate these concepts:

We then covered linear approximation (Sec 4.2), using FER #8 an example, and applied optimization (Sec 4.7), using FER #17 as an example:

Schedule

• WebWork: “Derivatives – Logarithmic” and “Derivatives – Implicit” extended to Fri Dec 13
• Final Exam Review: hand in written solutions to the following exercises on Wed Dec 11:
  • #5 (logarithmic differentiation)
  • #7 (implicit differentiation)
  • #8 (tangent lines, linear approximations and differentials)
  • #16 & #17 (optimization)
  • #18 (using critical pts, intervals of increasing/decreasing, and intervals of concavity for sketching a graph)
  • note that we will cover linear approximation/differentials and optimization on Monday, including setting up the exercises above
  • we have covered logarithmic differentiation, implicit differentiation, and the concepts of #18 — please complete those now
  • the Final Exam Review is available as a pdf on OpenLab Files
• Exam #3:
  • take-home exercises for this exam will be handed out in class on Wed Dec 11, to be handed in on Monday Dec 16
  • there will also be a short in-class exam on Monday Dec 16, similar to the take-home exercises
  • we will use half the class period on Mon Dec 16 to do some additional review for the final
• Final exam: Wednesday Dec 18

Boardshots

We continued the example from the previous class on graph-sketching using the first and second derivatives, looking at a cubic polynomial f(x):

• using the first derivative f'(x) to
  • find the critical points (where f'(x) = 0)
  • to figure out the intervals on which f(x) is increasing (which corresponds to where f'(x) > 0) vs the intervals on which f(x) is decreasing (where f'(x) < 0)
  • to classify each critical point as a local max or a local min
• using the second derivative f”(x) to
  • figure out the intervals on which f(x) is “concave up” (where f”(x) > 0) vs the intervals on which f(x) is “concave down” (where f”(x) < 0)
  • to find the inflection points (where the graph changes concavity)
• using this information to sketch the graph

Please look at the various figures in Sec 4.5 which illustrate these concepts: